arXiv subjects

Fuming Ma

Publications and source records attributed to Fuming Ma.

5 recordsLinked to original sources

arXiv2021

Inverse obstacle scattering for elastic waves in the time domain

This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value problem of the time domain Navier equation to a coupled initial-boundary value problem of wave equations, and prove the uniqueness of the solution for the coupled problem by employing energy method. The retarded single layer potential is introduced to establish the coupled boundary integral equations, and the uniqueness is discussed for the solution of the coupled boundary integral equations. Based on the convolution quadrature method for time discretization, the coupled boundary integral equations are reformulated into a system of boundary integral equations in s-domain, and then a convolution quadrature based nonlinear integral equation method is proposed for the inverse problem. Numerical experiments are presented to show the feasibility and effectiveness of the proposed method.

math.NA↗

arXiv2021

Computation of transmission eigenvalues by the regularized Schur complement for the boundary integral operators

This paper is devoted to the computation of transmission eigenvalues in the inverse acoustic scattering theory. This problem is first reformulated as a two by two boundary system of boundary integral equations. Next, utilizing the Schur complement technique, we develop a Schur complement operator with regularization to obtain a reduced system of boundary integral equations. The Nystr\"{o}m discretization is then used to obtain an eigenvalue problem for a matrix. We employ the recursive integral method for the numerical computation of the matrix eigenvalue. Numerical results show that the proposed method is efficient and reduces computational costs.

math.NA↗

arXiv2019

Numerical schemes to reconstruct three dimensional time-dependent point sources of acoustic waves

This paper is concerned with the numerical simulation of three dimensional time-dependent inverse source problems of acoustic waves. The reconstructions of both multiple stationary point sources and a moving point source are considered. The modified method of fundamental solutions (MMFS), which expands the solution utilizing the time convolution of the Green's function and the signal function, is proposed to solve the problem. For the reconstruction of a moving point source, moreover, the MMFS is simplified as a simple sampling method at each time step. Numerical experiments are provided to show the effectiveness of the proposed methods.

math.NA↗

arXiv2018

Analysis of the time domain acoustic scattering from open cavities

This paper is concerned with the analysis of the time domain acoustic scattering from two-dimensional open cavities. A transparent boundary condition is developed to reformulate the scattering problem into an equivalent initial boundary value problem in the interior domain of the open cavity. The well-posedness, that is, the existence, uniqueness and stability of the solution to the reduced problem are studied via a "Laplace domain" to time domain analysis. Moreover, time domain boundary integral equations for the reduced problem are established.

math.AP↗

arXiv2017

Solving the multi-frequency electromagnetic inverse source problem by the Fourier method

This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and the polarization vector decomposition, we propose a novel method for determining the source function in the full vector Maxwell's system. Rigorous mathematical justifications of the method are given and numerical examples are provided to demonstrate the feasibility and effectiveness of the method.

math.NA↗